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andriy [413]
2 years ago
6

Find the total area for the regular pyramid.

Mathematics
1 answer:
hram777 [196]2 years ago
3 0

Answer:

  • Option B

Step-by-step explanation:

Given is the hexagonal pyramid.

We know the radius of the base is same as its side.

<u>Find the base area:</u>

  • A = 3√3/2a²
  • A = 3√3/2*6² = 54√3

<u>Given the height and radius, find the side of the lateral triangular faces:</u>

  • \sqrt{8^2+6^2} =\sqrt{100} =10

Each of 6 triangles have sides 10, 10 and 6 units.

<u>Find the area using heron's formula:</u>

  • s = P/2 = (10*2 + 6)/2 = 13
  • s - a = s - b = 13 - 10 = 3
  • s - c = 13 - 6 = 7
  • A = \sqrt{s(s-a)(s-b)(s-c)} =\sqrt{13*3*3*7} =3\sqrt{91}

<u>Total surface area:</u>

  • S = 6*3\sqrt{91}+54\sqrt{3}  =18\sqrt{91}+54\sqrt{3}

Correct choice is B

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Answer:

According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02

Step-by-step explanation:

We are given the following data in the question:

10, 11, 12, 13, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19, 20

Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{225}{15} = 15

Sum of squares of differences = 25 + 16 + 9 + 4 + 4+ 4 + 1 + 0+ 1+ 1 + 4 + 9 + 9+ 16 + 25 = 128

S.D = \sqrt{\dfrac{128}{14}} = 3.02

Empirical rule:

  • According to this rule almost all the data lies within three standard deviation of the mean for a normal distribution.
  • About 68% of data lies within one standard deviation of the mean.
  • About 95% of data lies within two standard deviations of mean.
  • Arround 99.7% of data lies within three standard deviation of mean.

Thus, by empirical rule,

\mu \pm 1\sigma = 15\pm (3.02) = (11.98,18.02)

According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02

5 0
3 years ago
Jose’s school has 426 students. His principal has promised the Student Council that their idea will be carried out if they can g
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Answer: Step 4

<u>Step-by-step explanation:</u>

1. Define variable x as student signatures still needed  (Correct)

2)\ \dfrac{x+82}{426}              (Correct)

3. 25% = 0.25      (Correct)

4)\ \dfrac{x+82}{426}\leq 0.25      (Error)!

The inequality symbol should be GREATER THAN or equal to (≥) because Jose needs 25% or more (not less).

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Answer:

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5×5×5=625

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8×8×8=512cm..

8 0
3 years ago
The projected sales volume of a video game cartridge is given by the function s(p) = 3000 / (2p + a), where s is the number of c
Alex_Xolod [135]

Answer: 149 cartridges will be sold at 20 dollars per cartridge.

Step-by-step explanation:

Given: The projected sales volume of a video game cartridge is given by the function s(p)=\dfrac{3000}{2p+a}, where <em>s</em> is the number of cartridges sold, in thousands; <em>p</em> is the price per cartridge, in dollars; and <em>a</em> is a constant.

Put s(p)=100000, p= 10, we get

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i.e. s(p)=\dfrac{3000}{2p-19.97}

Put p=20, we get

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Hence, 149 cartridges will be sold at 20 dollars per cartridge.

8 0
3 years ago
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Novosadov [1.4K]

3,500 is the best estimate if you multiply 7 by round 456 to 500 so 7x500=3,500

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